Smallest Positive Prime

Number Theory Level 4

Which is the smallest positive prime which is some multiple of seven less than a cube of a counting number less than ten ?


The answer is 7.

Vandit Kankariya by Vandit Kankariya , 21, India

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2 solutions

Bill Bell
Aug 2, 2015 
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from gmpy2 import is_prime

smallest_prime=10**8
cubes=[n**3 for n in range(1,10)]
for cube in cubes:
    upper_k=1+cube/7
    for k in range(1,upper_k):
        possible_prime=cube-7*k
        if is_prime(possible_prime) and smallest_prime>possible_prime:
            smallest_prime=possible_prime
            associated_cube=cube
            associated_k=k
print smallest_prime

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Vandit Kankariya
Mar 30, 2014

7^3 -(7 × 48) = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The wordings are quite a "lot" misleading. Why shan't I read it as "some multiple of ( n 3 − 7 n^3-7 )?

Satvik Golechha - 6 years, 10 months ago

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